How would you model 'a sphere with a shell' like object?
Just create your sphere and over it draw the shape of your cuts using a Bezier Curve object.

Adjust its shape as necessary, then use knife project to cut the shape.



In object mode select your curve, then without deselecting, select your sphere, by this specific order. Enter edit mode on the sphere and with all faces selected use Knife Project with the option Cut Through active.



Carefully select all the unwanted parts then remove them by deleting the faces.